Small space satellites can be used for a large variety of applications. One issue with small space satellites involves the ability to quickly and accurately retarget the satellite, e.g., to aim an element of the satellite (e.g., a communications transmitter or receiver, a camera, a laser, etc.) at a target (e.g., a terrestrial- or space-based target).
The following references are cited throughout this patent application, each of which is hereby incorporated herein by reference:
Reference 1. Patankar K., Normal Fitz-Coy, and Roithmayr, C., “Design Considerations for Miniaturized Control Moment Gyroscopes for Rapid Retargeting and Precision Pointing of Small Satellites,” Proceedings of the 28th Annual AIAA/USU Conference on Small Satellites, Logan, Utah, August 2014.
Reference 2. Wie, B., Bailey, D., and Heiberg C., “Singularity Robust Steering Logic for Redundant Single-Gimbal Control Moment Gyros,” Journal of Guidance, Control & Dynamics, Vol. 24, No. 5, September-October 2001.
Reference 3. Garg, D., Patterson, M., Hager W., Rao, A., Benson, D., Huntington, G., “An Overview of Three Pseudospectral Methods for the Numerical Solution of Optimal Control Problems,” AAS-09-332, 2009.
Reference 4. Patterson, M., and Rao, A., “GPOPS-ii Version 2.0: A General-Purpose MATLAB Software for Solving Multiple-Phase Optimal Control Problems,” ttp://www.gpops2.com. May 2014.
Reference 5. BridgeSat Inc., http://www.bridgesatinc.com.
Reference 6. Gill, P., Murray W., and Saunders M., “SNOPT: An SQP algorithm for Large-scale Constrained Optimization,” SIAM Review 47, 1, 99-131, 2002.
Reference 7. Ross, M. and Karpenko M., “A Review of Pseudospectral Optimal Control: From Theory to Flight”, Annual Review in Control 36, 182-197, 2012.
Reference 8. Betts, J., “Practical Methods for Optimal Control and Estimation Using Nonlinear Programming”, SIAM Series in Advances in Design and Control, Chapter 2.
Reference 9. Maes, C., “A Regularized Active-Set Method for Sparse Convex Quadratic Programming”, Ph.D. Dissertation, Stanford, November 2010.
Reference 10. Davis T., “Direct Methods for Sparse Linear Systems”, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 2006.
Reference 11. Wright and Nocedal, “Numerical Optimization”, 2nd Edition, Springer Science+Business Media, LLC, New York, N.Y., 2006.
Reference 12. U.S. Pat. No. 8,880,246 entitled “Method and Apparatus for Determining Spacecraft Maneuvers,” Nov. 4, 2014.
Reference 13. Yoon, H. and Panagiotis, T., “Singularity Analysis of Variable-Speed Control Moment Gyros”, Journal of Guidance, Control, and Dynamics, Vol. 27, No. 3, May-June 2004, pp. 374-386.
Rapid retargeting and precision pointing of small satellites has drawn great interest as laser communication networks using Low Earth Orbit (LEO) constellations of small satellites has arisen as a potential alternative to already saturated RF communication [see Reference 5]. This new commercial application, as well as other applications, such as high-resolution imaging and Earth and space monitoring [see Reference 1], significantly increases the need for agile and high precision satellites. In particular, the ability to perform rapid slew and settle maneuvers can have many advantages, such as, for example, increasing productivity or revenue (e.g., allowing the satellite to capture a larger number of images in a given period of time or to increase the number or duration of communication connections) and decreasing satellite power consumption (which can increase mission time). Thus, time-optimal (shortest-time) attitude control maneuvers are desirable.
Satellite attitude control systems commonly involve Eigen axis rotations. Eigen axis rotations are desirable as they are intuitively simple to construct and provide the advantage of reorienting the spacecraft along the shortest circular arc between the starting and desired final attitude angles. The angular error defined by translation from a first orientation to a second orientation can be represented as rotation through a certain angle about a particular fixed axis, referred to as the Eigen axis of the rotation. Once the Eigen axis has been determined, two other axes that need not be aligned with the reference spacecraft body fixed frame may be selected to form an orthogonal set with the Eigen axis. Since the entire rotation from the initial to the final states is performed about the Eigen axis, the other two axes will always have zero angles to be traversed. Eigen axis rotations are normally implemented as rest-to-rest maneuvers. That is, the rotation is initiated from rest and terminated when the spacecraft is again at rest in the new desired orientation. A maneuver similar to an Eigen axis rotation can be constructed when it is desired to initiate a reorientation maneuver from a non-resting state and/or when it is desired to terminate a reorientation maneuver at a non-resting state. For such non-rest maneuvers, rotations will normally be carried out as simultaneous rotations about three orthogonal axes and designed similarly to an Eigen axis maneuver according to the kinematic differential equations. In some satellite retargeting systems, fast retargeting and precision pointing are achieved by a combination of two different kinds of actuators, control moment gyros (CMGs) and reaction wheels (RWs). During slew, the CMGs are employed and the RWs are employed during settle and pointing.
CMGs present a unique challenge for performing satellite retargeting. In particular, unlike an array of reaction wheels, for which the torque capability is fixed with respect to the satellite frame, the torque capability of a CMG array varies continuously with the gimbal angles. Consequently, ensuring accurate torque production on the satellite requires proper configuration of the CMGs relative to one another, for example, to avoid gimbal configurations that result in singular states wherein torque cannot be produced in a certain direction. CMGs also have gimbal rate and input torque constraints that can be violated during the operation of the satellite, particularly if the satellite angular rates exceed predetermined limits, potentially leading to a loss of control of the satellite. Because of these complexities, devising a mechanism to ensure the predictability of shortest-time and other desired reorientations or maneuvers is an important aspect of the maneuver design problem for CMG-based satellite retargeting systems. Accordingly, improved methods and apparatus are needed for determining and implementing satellite retargeting maneuvers while maintaining operation within torque and other physical or operational limits.
During pointing, RWs may become ineffective as their spin rates reach the maximum rate. They require frequent momentum dumping, which effectively means reducing spin rates with additional actuators such as magnetic rods.
Furthermore, the use of separate CMG and RW actuators can make it difficult to meet strict size, weight, and power (SWaP) constraints that often exist for small satellites, especially where three or four sets of CMG and/or RW actuators are often used in order to control motion around multiple axes. As investigated in detail by Reference 1, such SWaP requirements can be met in many cases by miniaturized CMGs with integral variable speed flywheels (equivalently, RWs) capable of precisely controlled spinning. This type of CMG effectively combines typical CMG and RW actuators and is referred to herein as a “hybrid control moment gyroscope” or “HCMG.”
The HCMG is a promising technology to enable rapid retargeting and precision pointing. However, it may suffer from old disadvantages inherited from the CMG and new disadvantages created by combining the CMG and RW. The former includes the well-known CMG gimbal singularity [see Reference 13], and the latter includes RW controllability. RW controllability is simply determined by the RW orientation. Typically, the RW orientation is fixed, but in the HCMG case, it varies and is determined by the gimbal angles.
The singularities related to the HCMG have been addressed by an extended singularity avoidance steering logic [see Reference 1, Reference 2, Reference 13]. Such singularity avoidance steering logic is an effective way to avoid the singularities but may not be an efficient way to enable rapid retargeting due to artificially inserted perturbation terms.